Paul Ryan repeatedly grilled about his support for Donald Trump at a town-hall event

Screenshot/CNN House Speaker Paul Ryan emphatically attempted to justify his support for Donald Trump on Tuesday, calling the coming presidential election "a binary choice" in which he must overlook some of Trump's less-popular positions.

Audience members at a CNN town-hall event in New York repeatedly grilled Ryan on his tepid support for the presumptive Republican nominee, at times getting into testy exchanges.

One person challenged Ryan on Trump's proposal to bar Muslims from entering the US, an idea for which Ryan has criticized Trump.

"How do you explain to the 1.6 billion Muslims that we trade with, that we ally with, that live next door to us, how you endorse a man who has that proposal on his agenda?" a woman asked.

"We have a binary choice — Donald Trump, Hillary Clinton. I pick Donald Trump," Ryan responded. "We don't have people who run for office who 100% reflect all of our views. It doesn't work like that. We have to find people who reflect most of our views and whose views are more reflective of our views than the other candidate."

Another audience member, a Republican student who said he would not vote for Trump, questioned how Ryan could "morally support" a candidate who the student said was "openly racist and has made Islamophobic statements."

The conversation soon shifted to the Republican National Convention, which kicks off next week in Cleveland. New Jersey Republican Steve Lonegan — a leader in the effort to "unbind" Republican delegates from their states' primary results, asked Ryan whether he would support an "open convention" in which delegates could "vote their conscience" in hopes of nominating another candidate.

Steve Lonegan. AP Photo/Mel Evans

"It is not my job as chairman of the convention to tell the delegates how to run their convention," Ryan said. "It is my job to take the rules that they write for the convention and make sure that those rules are applied equally, honestly, and transparently."

Ryan shot back: "My answer is no, I'm not going to tell the delegates what to do. It is their decision because they run the party."

Lonegan answered, "I'd just like to remind you, Mr. Speaker, that as a bottom-up party, we have a representative form of government in which the delegates also represent the 75% of Republicans who did not vote for Donald Trump."

The Convention Rules Committee will meet tomorrow to discuss whether to amend the rules on how delegates may vote.